Hidenori Murakami - Academia.edu (original) (raw)

Papers by Hidenori Murakami

Volume 6B: Energy, 2015

Large offshore renewable energy investments require the use of maintenance boats to keep them in ... more Large offshore renewable energy investments require the use of maintenance boats to keep them in operable conditions. Unfortunately, due to rough seas in some of the project locations, the transferring of crew members from vessel to turbine or platform is no easy task. Thus, the research presented is focused at further looking into add on stability systems for marine vessels to further ease the process of offshore platform maintenance and crew member safety. The rolling and pitching of ships and boats induced by the ocean waves results in undesirable motion. In an effort to increase the stability of the deck/platform and human comfort and safety, various add-on stability systems have been developed. Of interest in the research presented are internal active systems, specifically the active gyroscopic stabilizer. Previous research and industrial use of active gyroscopic roll stabilizers has shown and proven the effectiveness of the system to reduce rolling motion. The research present...

In order to develop an active nonlinear beam model, the beam’s kinematics is examined by employin... more In order to develop an active nonlinear beam model, the beam’s kinematics is examined by employing the kinematic assumption of a rigid cross section during deformation. As a mathematical tool, the moving frame method, developed by Elie Cartan (1869–1951) on differentiable manifolds, is utilized by treating a beam as a frame bundle on a deforming centroidal curve. As a result, three new integrability conditions are obtained, which play critical roles in the derivation of beam equations of motion. They also serve a role in a geometrically-exact finite-element implementation of beam models. These integrability conditions enable the derivation of beam models starting from the three-dimensional Hamilton’s principle and the d’Alembert principle of virtual work. Finally, the reconstruction scheme for rotation matrices for given angular velocity at each time is presented.Copyright © 2016 by ASME

Volume 4B: Dynamics, Vibration, and Control, 2015

To describe the configuration of a multi-body system, Cartesian coordinate systems are attached t... more To describe the configuration of a multi-body system, Cartesian coordinate systems are attached to all bodies comprising the system. Their connections through joints and force elements are efficiently expressed by using 4×4 matrices of the homogeneous transformation, presented by Denavit and Hartenberg in 1955. However, at this time, there is no systematic method to compute velocities and angular velocities using the matrices of such homogeneous transformations. In this paper, homogeneous transformation matrices are identified as a subset of a Lie group, called the special Euclidean group denoted by SE(3). This observation enables the usage of the Lie group theory in multibody kinematics. The effective use of the theory is built upon a platform of a moving frame method as presented in this paper. In this method, for each body-attached Cartesian coordinate system, the coordinate vector basis is written explicitly following Élie Cartan. This moving frame notation enables us to use the...

Transactions of the Japan Society of Mechanical Engineers, 1974

Journal of Applied Mechanics, 2017

Utilizing the kinematics, presented in the Part I, an active large deformation beam model for sle... more Utilizing the kinematics, presented in the Part I, an active large deformation beam model for slender, flexible, or soft robots is developed from the d'Alembert's principle of virtual work, which is derived for three-dimensional elastic solids from Hamilton's principle. This derivation is accomplished by refining the definition of the Cauchy stress tensor as a vector-valued 2-form to exploit advanced geometrical operations available for differential forms. From the three-dimensional principle of virtual work, both the beam principle of virtual work and beam equations of motion with consistent boundary conditions are derived, adopting the kinematic assumption of rigid cross sections of a deforming beam. In the derivation of the beam model, Élie Cartan's moving frame method is utilized. The resulting large deformation beam equations apply to both passive and active beams. The beam equations are validated with the previously reported results expressed in vector form. To...

Journal of Applied Mechanics, 2017

In order to develop an active nonlinear beam model, the beam's kinematics is examined in this... more In order to develop an active nonlinear beam model, the beam's kinematics is examined in this paper, by employing the kinematic assumption of a rigid cross section during deformation. As a mathematical tool, the moving frame method, developed by Cartan (1869–1951) on differentiable manifolds, is utilized by treating a beam as a frame bundle on a deforming centroidal curve. As a result, three new integrability conditions are obtained, which play critical roles in the derivation of beam equations of motion. These integrability conditions enable the derivation of beam models in Part II, starting from the three-dimensional Hamilton's principle and the d'Alembert's principle of virtual work. To illustrate the critical role played by the integrability conditions, the variation of kinetic energy is computed. Finally, the reconstruction scheme for rotation matrices for given angular velocity at each time is presented.

International Journal of Solids and Structures, 1987

ABSTRACT In order to improve the accuracy of the in-plane responses of the shear deformable lamin... more ABSTRACT In order to improve the accuracy of the in-plane responses of the shear deformable laminated composite plate theories, a new high-order laminated plate theory was developed based upon Reissner's new mixed variational principle [Int. J. Num. Meth. Eng.20, 1366 (1984)]. To this end, a zig-zag shaped C0 function and Legendre polynomials were introduced into the approximate in-plane displacement distributions across the plate thickness. The accuracy of the present theory was examined by applying it to the cylindrical bending problem of laminated plates which had been solved exactly by Pagano [J. Comp. Mat.3, 398 (1969)]. A comparison with the exact solutions obtained for several symmetric and asymmetric cross-ply laminates indicates that the present theory accurately estimates in-plane responses, even for small span-to-thickness ratios.

Volume 4A: Dynamics, Vibration, and Control, 2016

We consider the torque-free rotation of a rigid body with three distinct moment of inertia values... more We consider the torque-free rotation of a rigid body with three distinct moment of inertia values and angular velocity components. As can be seen in the Dzhanibekov and tennis racket phenomena, rotations about the largest and smallest principal moments of inertia create stable rotations. However, when rotating about the principal intermediate moment of inertia, an unstable rotation is produced that leads to the basis of this phenomena. In this publication, the above phenomena are examined and explained analytically and applied to a satellite system to observe the change in trajectory as the solar panels and reflectors are deployed. To begin the derivation, the Euler torque-free equations for a rotating rigid body are formulated using the moving frame method. The derived equations are then non-dimensionalized and a complete analytical solution, including an expression for the non-dimensional period, is presented. Second, we further look at the limiting axisymmetric cases and examine ...

Volume 4A: Dynamics, Vibration, and Control, 2016

Due to the advent of pneumatic actuators, tendon-actuation mechanisms, and artificial muscles, an... more Due to the advent of pneumatic actuators, tendon-actuation mechanisms, and artificial muscles, an increasing number of robot engineers are developing flexible and soft robots. The emergence of soft and flexible robotics has offered new methods of locomotion that have applications in a wide variety of sectors. The research presented here focuses on developing mechanical models for such flexible robots. Two models are developed that will aid the modeling of soft robotics: (i) a discrete multi-body model consisting of jointed cylindrical segments and (ii) a thorough continuous beam model with internal actuation. The mechanical models serve as indicators of the necessary internal actuation for soft robots to reproduce or mimic the observed or necessary motion.Copyright © 2016 by ASME

Volume 4A: Dynamics, Vibration, and Control, 2015

In this paper, we present complete explanation of the Dzhanibekov phenomenon demonstrated in a sp... more In this paper, we present complete explanation of the Dzhanibekov phenomenon demonstrated in a space station (www.youtube.com/watch?v=L2o9eBl_Gzw) and the tennis racket phenomenon (www.youtube.com/watch?v=4dqCQqI-Gis). These phenomena are described by Euler’s equation of an unconstrained rigid body that has three distinct values of moments of inertia. In the two phenomena, the rotations of a body about the principal axes that correspond to the largest and the smallest moments of inertia are stable. However, the rotation about the axis corresponding to the intermediate principal moment of inertia becomes unstable, leading to the unexpected rotations that are the basis of the phenomena. If this unexpected rotation is not explained from a complete perspective which accounts for the relevant physical and mathematical aspects, one might misconstrue the phenomena as a violation of the conservation of angular momenta. To address this, especially for students, we investigate the phenomena u...

International Journal of Solids and Structures, 1998

ABSTRACT Using a semi-analytical finite element (FE) method, the torsional phase velocity spectra... more ABSTRACT Using a semi-analytical finite element (FE) method, the torsional phase velocity spectra of elastic waves were investigated for reinforced concrete (RC) columns with and without exterior composite layers. An examination of the spectra of these two types of columns shows that the retrofitted columns have a slightly smaller phase velocity in their first mode. In addition, the first mode shapes exhibit marked warping induced by the vertical bars.Comparisons of the exact phase velocity of the first mode with those calculated from elementary theories indicate that the elementary theories give a poor prediction of the torsional wave speed even at the long wavelength limit. This inaccuracy, which comes from not including the effect of warping, can be overcome by computing the torsional rigidity utilizing Saint-Venant's semi-inverse method for torsional warping.

International Journal of Solids and Structures, 2001

... Part II. Quasi-static analysis. ... It is concluded that infinitesimal mechanism modes and pr... more ... Part II. Quasi-static analysis. ... It is concluded that infinitesimal mechanism modes and pre-stresses characterize the static and dynamic response of tensegrity ... In order to examine static and kinematic determinancy of structures, small deformation equilibrium equations have been ...

Mechanics of Materials, 1998

... The average length of fibers was 142 mm and the average cross sectional geometry was characte... more ... The average length of fibers was 142 mm and the average cross sectional geometry was characterized by a rectangle of 0.73×0.13 mm. (Under uniaxial tension tests, SIMCON fibers exhibit an elastic–plastic stress–strain relation of the Ramberg–Osgood type.) Cement-based ...

In response to the need for an advanced computational model for nonlinear wave propagation in fib... more In response to the need for an advanced computational model for nonlinear wave propagation in fiber-reinforced composites, a new finite element is developed for unidirectionally fiber-reinforced composites. The element is a numerical implementation of the higher-order homogenization model proposed by Murakami and Hegemier (1986) extended to encompass nonlinear material response. Due to dispersion and attenuation effects induced by regularly spaced fibers, wave phenomena in the composites are altered significantly. In the model, the deformation in a heterogeneous composite domain is described by average displacement fields for both fiber and matrix along with the higher order microstructural displacements. The accuracy and efficacy of the new element is investigated by applying it to waveguide and wave-reflect problems of a composite half-space and comparing the wave response with that of DYNA2D (Hallquist, 1982). The analyses by DYNA2D discretize explicitly the details of the hetero...

Computational Mechanics ’88, 1988

The mixture theory proposed by Murakami and Hegemier [1] is applied to the transient dynamic anal... more The mixture theory proposed by Murakami and Hegemier [1] is applied to the transient dynamic analysis of elastoplastic fiber reinforced composites. The model is based on the two scale-asymptotic expansions as described by Bensoussan, Lions and Papanicolaou [2], and Sanchez-Palencia [3]. Equations of motion are obtained from the principle of virtual work, while the appropriate incremental constitutive equations are deduced from Reissner’s [4] mixed variational principle. The finite element method is used for the spatial discretization. The resulting semi-discrete equations of motion are then integrated using the explicit method. The fibers are assumed elastic, while the matrix obeys a von Mises yield criterion with linear hardening. A semi-infinite fiber reinforced composite under a step pressure is considered. Stress profiles show the dispersive nature of the waves in the composite.

Journal of Terramechanics, 1992

Journal of Engineering Mechanics, 1997

The effect of constitutive coupling of stretching, bending, and transverse shearing on the free v... more The effect of constitutive coupling of stretching, bending, and transverse shearing on the free vibration of anisotropic cantilever beams as well as simply supported beams with narrow rectangular cross sections was investigated. To this end, a Timoshenko-type beam theory was constructed for plane deformation of anisotropic beams by incorporating Reissner's semicomplementary energy function in a Hamilton-type principle. By using the resulting beam equations, natural frequencies and mode shapes were computed. The numerical results illustrate the importance of correctly accounting for anisotropy in obtaining natural frequencies and show dramatic normal-shear coupling effects for mode shapes.

Journal of Energy Resources Technology, 1991

An asymptotic mixture theory of fiber-reinforced composites with periodic microstructure is prese... more An asymptotic mixture theory of fiber-reinforced composites with periodic microstructure is presented for rate-independent inelastic responses, such as elastoplastic deformation. Key elements are the modeling capability of simulating critical interaction across material interfaces and the inclusion of the kinetic energy of micro-displacements. The construction of the proposed mixture model, which is deterministic, instead of phenomenological, is accomplished by resorting to a variational approach. The principle of virtual work is used for total quantities to derive mixture equations of motion and boundary conditions, while Reissner’s mixed variational principle (1984, 1986), applied to the incremental boundary value problem yields consistent mixture constitutive relations. In order to assess the model accuracy, numerical experiments were conducted for static and dynamic loads. The prediction of the model in the time domain was obtained by an explicit finite element code. DYNA2D is u...

Journal of Applied Mechanics, 2000

In order to develop an accurate one-dimensional model for wave propagation in heterogeneous beams... more In order to develop an accurate one-dimensional model for wave propagation in heterogeneous beams with uniform cross sections, a Hamilton-type principle is developed by incorporating Reissner’s semi-complimentary energy function. Trial displacement and transverse stress fields are constructed from the solutions of micro-boundary value problems (MBVP’s) defined over the cross section. The MBVP’s are developed from asymptotic expansions that assume a small diameter cross section compared to the axial length and a typical signal wavelength. Saint Venant’s semi-inverse torsion and flexure problems are included in the system of MBVP’s. By utilizing the displacement and transverse stress fields constructed from the numerical solutions of the MBVP’s, the constitutive relations are developed. The model generalizes the Mindlin-Hermann rod model and the Timoshenko beam model for anisotropic heterogeneous beams. The accuracy of the model is assessed by comparing the predicted phase velocity sp...

Volume 6B: Energy, 2015

Large offshore renewable energy investments require the use of maintenance boats to keep them in ... more Large offshore renewable energy investments require the use of maintenance boats to keep them in operable conditions. Unfortunately, due to rough seas in some of the project locations, the transferring of crew members from vessel to turbine or platform is no easy task. Thus, the research presented is focused at further looking into add on stability systems for marine vessels to further ease the process of offshore platform maintenance and crew member safety. The rolling and pitching of ships and boats induced by the ocean waves results in undesirable motion. In an effort to increase the stability of the deck/platform and human comfort and safety, various add-on stability systems have been developed. Of interest in the research presented are internal active systems, specifically the active gyroscopic stabilizer. Previous research and industrial use of active gyroscopic roll stabilizers has shown and proven the effectiveness of the system to reduce rolling motion. The research present...

In order to develop an active nonlinear beam model, the beam’s kinematics is examined by employin... more In order to develop an active nonlinear beam model, the beam’s kinematics is examined by employing the kinematic assumption of a rigid cross section during deformation. As a mathematical tool, the moving frame method, developed by Elie Cartan (1869–1951) on differentiable manifolds, is utilized by treating a beam as a frame bundle on a deforming centroidal curve. As a result, three new integrability conditions are obtained, which play critical roles in the derivation of beam equations of motion. They also serve a role in a geometrically-exact finite-element implementation of beam models. These integrability conditions enable the derivation of beam models starting from the three-dimensional Hamilton’s principle and the d’Alembert principle of virtual work. Finally, the reconstruction scheme for rotation matrices for given angular velocity at each time is presented.Copyright © 2016 by ASME

Volume 4B: Dynamics, Vibration, and Control, 2015

To describe the configuration of a multi-body system, Cartesian coordinate systems are attached t... more To describe the configuration of a multi-body system, Cartesian coordinate systems are attached to all bodies comprising the system. Their connections through joints and force elements are efficiently expressed by using 4×4 matrices of the homogeneous transformation, presented by Denavit and Hartenberg in 1955. However, at this time, there is no systematic method to compute velocities and angular velocities using the matrices of such homogeneous transformations. In this paper, homogeneous transformation matrices are identified as a subset of a Lie group, called the special Euclidean group denoted by SE(3). This observation enables the usage of the Lie group theory in multibody kinematics. The effective use of the theory is built upon a platform of a moving frame method as presented in this paper. In this method, for each body-attached Cartesian coordinate system, the coordinate vector basis is written explicitly following Élie Cartan. This moving frame notation enables us to use the...

Transactions of the Japan Society of Mechanical Engineers, 1974

Journal of Applied Mechanics, 2017

Utilizing the kinematics, presented in the Part I, an active large deformation beam model for sle... more Utilizing the kinematics, presented in the Part I, an active large deformation beam model for slender, flexible, or soft robots is developed from the d'Alembert's principle of virtual work, which is derived for three-dimensional elastic solids from Hamilton's principle. This derivation is accomplished by refining the definition of the Cauchy stress tensor as a vector-valued 2-form to exploit advanced geometrical operations available for differential forms. From the three-dimensional principle of virtual work, both the beam principle of virtual work and beam equations of motion with consistent boundary conditions are derived, adopting the kinematic assumption of rigid cross sections of a deforming beam. In the derivation of the beam model, Élie Cartan's moving frame method is utilized. The resulting large deformation beam equations apply to both passive and active beams. The beam equations are validated with the previously reported results expressed in vector form. To...

Journal of Applied Mechanics, 2017

In order to develop an active nonlinear beam model, the beam's kinematics is examined in this... more In order to develop an active nonlinear beam model, the beam's kinematics is examined in this paper, by employing the kinematic assumption of a rigid cross section during deformation. As a mathematical tool, the moving frame method, developed by Cartan (1869–1951) on differentiable manifolds, is utilized by treating a beam as a frame bundle on a deforming centroidal curve. As a result, three new integrability conditions are obtained, which play critical roles in the derivation of beam equations of motion. These integrability conditions enable the derivation of beam models in Part II, starting from the three-dimensional Hamilton's principle and the d'Alembert's principle of virtual work. To illustrate the critical role played by the integrability conditions, the variation of kinetic energy is computed. Finally, the reconstruction scheme for rotation matrices for given angular velocity at each time is presented.

International Journal of Solids and Structures, 1987

ABSTRACT In order to improve the accuracy of the in-plane responses of the shear deformable lamin... more ABSTRACT In order to improve the accuracy of the in-plane responses of the shear deformable laminated composite plate theories, a new high-order laminated plate theory was developed based upon Reissner's new mixed variational principle [Int. J. Num. Meth. Eng.20, 1366 (1984)]. To this end, a zig-zag shaped C0 function and Legendre polynomials were introduced into the approximate in-plane displacement distributions across the plate thickness. The accuracy of the present theory was examined by applying it to the cylindrical bending problem of laminated plates which had been solved exactly by Pagano [J. Comp. Mat.3, 398 (1969)]. A comparison with the exact solutions obtained for several symmetric and asymmetric cross-ply laminates indicates that the present theory accurately estimates in-plane responses, even for small span-to-thickness ratios.

Volume 4A: Dynamics, Vibration, and Control, 2016

We consider the torque-free rotation of a rigid body with three distinct moment of inertia values... more We consider the torque-free rotation of a rigid body with three distinct moment of inertia values and angular velocity components. As can be seen in the Dzhanibekov and tennis racket phenomena, rotations about the largest and smallest principal moments of inertia create stable rotations. However, when rotating about the principal intermediate moment of inertia, an unstable rotation is produced that leads to the basis of this phenomena. In this publication, the above phenomena are examined and explained analytically and applied to a satellite system to observe the change in trajectory as the solar panels and reflectors are deployed. To begin the derivation, the Euler torque-free equations for a rotating rigid body are formulated using the moving frame method. The derived equations are then non-dimensionalized and a complete analytical solution, including an expression for the non-dimensional period, is presented. Second, we further look at the limiting axisymmetric cases and examine ...

Volume 4A: Dynamics, Vibration, and Control, 2016

Due to the advent of pneumatic actuators, tendon-actuation mechanisms, and artificial muscles, an... more Due to the advent of pneumatic actuators, tendon-actuation mechanisms, and artificial muscles, an increasing number of robot engineers are developing flexible and soft robots. The emergence of soft and flexible robotics has offered new methods of locomotion that have applications in a wide variety of sectors. The research presented here focuses on developing mechanical models for such flexible robots. Two models are developed that will aid the modeling of soft robotics: (i) a discrete multi-body model consisting of jointed cylindrical segments and (ii) a thorough continuous beam model with internal actuation. The mechanical models serve as indicators of the necessary internal actuation for soft robots to reproduce or mimic the observed or necessary motion.Copyright © 2016 by ASME

Volume 4A: Dynamics, Vibration, and Control, 2015

In this paper, we present complete explanation of the Dzhanibekov phenomenon demonstrated in a sp... more In this paper, we present complete explanation of the Dzhanibekov phenomenon demonstrated in a space station (www.youtube.com/watch?v=L2o9eBl_Gzw) and the tennis racket phenomenon (www.youtube.com/watch?v=4dqCQqI-Gis). These phenomena are described by Euler’s equation of an unconstrained rigid body that has three distinct values of moments of inertia. In the two phenomena, the rotations of a body about the principal axes that correspond to the largest and the smallest moments of inertia are stable. However, the rotation about the axis corresponding to the intermediate principal moment of inertia becomes unstable, leading to the unexpected rotations that are the basis of the phenomena. If this unexpected rotation is not explained from a complete perspective which accounts for the relevant physical and mathematical aspects, one might misconstrue the phenomena as a violation of the conservation of angular momenta. To address this, especially for students, we investigate the phenomena u...

International Journal of Solids and Structures, 1998

ABSTRACT Using a semi-analytical finite element (FE) method, the torsional phase velocity spectra... more ABSTRACT Using a semi-analytical finite element (FE) method, the torsional phase velocity spectra of elastic waves were investigated for reinforced concrete (RC) columns with and without exterior composite layers. An examination of the spectra of these two types of columns shows that the retrofitted columns have a slightly smaller phase velocity in their first mode. In addition, the first mode shapes exhibit marked warping induced by the vertical bars.Comparisons of the exact phase velocity of the first mode with those calculated from elementary theories indicate that the elementary theories give a poor prediction of the torsional wave speed even at the long wavelength limit. This inaccuracy, which comes from not including the effect of warping, can be overcome by computing the torsional rigidity utilizing Saint-Venant's semi-inverse method for torsional warping.

International Journal of Solids and Structures, 2001

... Part II. Quasi-static analysis. ... It is concluded that infinitesimal mechanism modes and pr... more ... Part II. Quasi-static analysis. ... It is concluded that infinitesimal mechanism modes and pre-stresses characterize the static and dynamic response of tensegrity ... In order to examine static and kinematic determinancy of structures, small deformation equilibrium equations have been ...

Mechanics of Materials, 1998

... The average length of fibers was 142 mm and the average cross sectional geometry was characte... more ... The average length of fibers was 142 mm and the average cross sectional geometry was characterized by a rectangle of 0.73×0.13 mm. (Under uniaxial tension tests, SIMCON fibers exhibit an elastic–plastic stress–strain relation of the Ramberg–Osgood type.) Cement-based ...

In response to the need for an advanced computational model for nonlinear wave propagation in fib... more In response to the need for an advanced computational model for nonlinear wave propagation in fiber-reinforced composites, a new finite element is developed for unidirectionally fiber-reinforced composites. The element is a numerical implementation of the higher-order homogenization model proposed by Murakami and Hegemier (1986) extended to encompass nonlinear material response. Due to dispersion and attenuation effects induced by regularly spaced fibers, wave phenomena in the composites are altered significantly. In the model, the deformation in a heterogeneous composite domain is described by average displacement fields for both fiber and matrix along with the higher order microstructural displacements. The accuracy and efficacy of the new element is investigated by applying it to waveguide and wave-reflect problems of a composite half-space and comparing the wave response with that of DYNA2D (Hallquist, 1982). The analyses by DYNA2D discretize explicitly the details of the hetero...

Computational Mechanics ’88, 1988

The mixture theory proposed by Murakami and Hegemier [1] is applied to the transient dynamic anal... more The mixture theory proposed by Murakami and Hegemier [1] is applied to the transient dynamic analysis of elastoplastic fiber reinforced composites. The model is based on the two scale-asymptotic expansions as described by Bensoussan, Lions and Papanicolaou [2], and Sanchez-Palencia [3]. Equations of motion are obtained from the principle of virtual work, while the appropriate incremental constitutive equations are deduced from Reissner’s [4] mixed variational principle. The finite element method is used for the spatial discretization. The resulting semi-discrete equations of motion are then integrated using the explicit method. The fibers are assumed elastic, while the matrix obeys a von Mises yield criterion with linear hardening. A semi-infinite fiber reinforced composite under a step pressure is considered. Stress profiles show the dispersive nature of the waves in the composite.

Journal of Terramechanics, 1992

Journal of Engineering Mechanics, 1997

The effect of constitutive coupling of stretching, bending, and transverse shearing on the free v... more The effect of constitutive coupling of stretching, bending, and transverse shearing on the free vibration of anisotropic cantilever beams as well as simply supported beams with narrow rectangular cross sections was investigated. To this end, a Timoshenko-type beam theory was constructed for plane deformation of anisotropic beams by incorporating Reissner's semicomplementary energy function in a Hamilton-type principle. By using the resulting beam equations, natural frequencies and mode shapes were computed. The numerical results illustrate the importance of correctly accounting for anisotropy in obtaining natural frequencies and show dramatic normal-shear coupling effects for mode shapes.

Journal of Energy Resources Technology, 1991

An asymptotic mixture theory of fiber-reinforced composites with periodic microstructure is prese... more An asymptotic mixture theory of fiber-reinforced composites with periodic microstructure is presented for rate-independent inelastic responses, such as elastoplastic deformation. Key elements are the modeling capability of simulating critical interaction across material interfaces and the inclusion of the kinetic energy of micro-displacements. The construction of the proposed mixture model, which is deterministic, instead of phenomenological, is accomplished by resorting to a variational approach. The principle of virtual work is used for total quantities to derive mixture equations of motion and boundary conditions, while Reissner’s mixed variational principle (1984, 1986), applied to the incremental boundary value problem yields consistent mixture constitutive relations. In order to assess the model accuracy, numerical experiments were conducted for static and dynamic loads. The prediction of the model in the time domain was obtained by an explicit finite element code. DYNA2D is u...

Journal of Applied Mechanics, 2000

In order to develop an accurate one-dimensional model for wave propagation in heterogeneous beams... more In order to develop an accurate one-dimensional model for wave propagation in heterogeneous beams with uniform cross sections, a Hamilton-type principle is developed by incorporating Reissner’s semi-complimentary energy function. Trial displacement and transverse stress fields are constructed from the solutions of micro-boundary value problems (MBVP’s) defined over the cross section. The MBVP’s are developed from asymptotic expansions that assume a small diameter cross section compared to the axial length and a typical signal wavelength. Saint Venant’s semi-inverse torsion and flexure problems are included in the system of MBVP’s. By utilizing the displacement and transverse stress fields constructed from the numerical solutions of the MBVP’s, the constitutive relations are developed. The model generalizes the Mindlin-Hermann rod model and the Timoshenko beam model for anisotropic heterogeneous beams. The accuracy of the model is assessed by comparing the predicted phase velocity sp...